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Geometry

Math Academy official course import: Geometry

176 节课

课程大纲

  1. 1.Proof, Congruence, & Similarity
    1. 1.1.1. Proof
      1. 1
        Identifying Angle Postulates
      2. 2
        Identifying Angle Theorems
      3. 3
        Proving Alternate Angle Theorems
      4. 4
        Further Proving Alternate Angle Theorems
      5. 5
        Proving Consecutive Angle Theorems
      6. 6
        Further Proving Consecutive Angle Theorems
      7. 7
        Proving Perpendicular Line Theorems
      8. 8
        Further Proving Perpendicular Line Theorems
    2. 2.1.2. Transformations
      1. 1
        Translations of Geometric Figures
      2. 2
        Rotations of Geometric Figures
      3. 3
        Rotating Objects in the Coordinate Plane Using Functions
      4. 4
        Reflections of Geometric Figures in the Cartesian Plane
      5. 5
        Reflections of Figures Across Arbitrary Lines
      6. 6
        Dilations of Geometric Figures
      7. 7
        Dilations of Figures in the Coordinate Plane
      8. 8
        Stretches of Geometric Figures
      9. 9
        Combining Stretches of Geometric Figures
      10. 10
        Combining Geometric Transformations
      11. 11
        Reflective Symmetry
      12. 12
        Rotational Symmetry
    3. 3.1.3. Congruence
      1. 1
        The ASA Congruence Criterion
      2. 2
        The AAS Congruence Criterion
      3. 3
        The SAS Congruence Criterion
      4. 4
        The SSS Congruence Criterion
      5. 5
        The HL Congruence Criterion
      6. 6
        Combining Congruence Criteria for Triangles
      7. 7
        Rigid Motions and Congruence
      8. 8
        Properties of Congruence
      9. 9
        Proving Congruence Statements
    4. 4.1.4. Similarity
      1. 1
        Similarity and Similar Polygons
      2. 2
        Side Lengths and Angle Measures of Similar Polygons
      3. 3
        Areas of Similar Polygons
      4. 4
        Working With Areas of Similar Polygons
      5. 5
        Similarity Transformations
      6. 6
        The AA Similarity Criterion
      7. 7
        The SSS Similarity Criterion
      8. 8
        The SAS Similarity Criterion
      9. 9
        Combining Similarity Criteria for Triangles
      10. 10
        Proving Similarity Statements
      11. 11
        The Midpoint Theorem
      12. 12
        Proving the Midpoint Theorem
      13. 13
        The Triangle Proportionality Theorem
  2. 2.Circles & Radian Measure
    1. 1.2.1. Circles Essentials
      1. 1
        Circles
      2. 2
        Arcs, Segments, and Sectors of Circles
      3. 3
        The Circumference of a Circle
      4. 4
        Areas of Circles
      5. 5
        Central Angles and Arcs
      6. 6
        Calculating Arc Lengths of Circular Sectors
      7. 7
        Calculating Areas of Circular Sectors
      8. 8
        Further Calculating Areas of Sectors
      9. 9
        Problem Solving With Circles
      10. 10
        Circles Inscribed in Squares
      11. 11
        Squares Inscribed in Circles
    2. 2.2.2. Circle Theorems
      1. 1
        Inscribed Angles
      2. 2
        Problem-Solving With Inscribed Angles
      3. 3
        Thales' Theorem
      4. 4
        Angles in Inscribed Right Triangles
      5. 5
        Further Angles in Inscribed Right Triangles
      6. 6
        Inscribed Quadrilaterals
      7. 7
        Tangent Lines to Circles
      8. 8
        Tangent-Tangent Lines to Circles
      9. 9
        Secant-Secant Angles to Circles
      10. 10
        Secant-Tangent Angles to Circles
      11. 11
        The Tangent-Chord Theorem
      12. 12
        Circle Similarity
      13. 13
        Proving Circle Similarity
    3. 3.2.3. Radians
      1. 1
        Introduction to Radians
      2. 2
        Calculating Arc Length Using Radians
      3. 3
        Calculating Areas of Sectors Using Radians
      4. 4
        Trigonometric Ratios With Radians
  3. 3.Geometry in the Coordinate Plane
    1. 1.3.1. Coordinate Geometry
      1. 1
        Parallel Lines in the Coordinate Plane
      2. 2
        Finding Equations of Parallel Lines
      3. 3
        Perpendicular Lines in the Coordinate Plane
      4. 4
        Finding Equations of Perpendicular Lines
      5. 5
        Midpoints in the Coordinate Plane
      6. 6
        Partitioning Line Segments
      7. 7
        The Distance Formula
      8. 8
        The Shortest Distance Between a Point and a Line
      9. 9
        Calculating Perimeters in the Plane
      10. 10
        Calculating Areas of Rectangles in the Plane
      11. 11
        Calculating Areas of Triangles and Quadrilaterals in the Plane
    2. 2.3.2. Circles in the Coordinate Plane
      1. 1
        Circles in the Coordinate Plane
      2. 2
        Equations of Circles Centered at the Origin
      3. 3
        Equations of Circles
      4. 4
        Determining Circle Properties by Completing the Square
      5. 5
        Calculating Circle Intercepts
      6. 6
        Intersections of Circles with Lines
      7. 7
        Equations of Tangent Lines to Circles
      8. 8
        Perpendicular Bisectors of Diameters in the Coordinate Plane
      9. 9
        Perpendicular Bisectors of Chords
      10. 10
        Perpendicular Bisectors of Chords in the Coordinate Plane
      11. 11
        Thales' Theorem in the Coordinate Plane
  4. 4.Triangles, Quadrilaterals, & Trigonometry
    1. 1.4.1. Triangles
      1. 1
        The Exterior Angle Theorem
      2. 2
        The Pythagorean Theorem
      3. 3
        The 45-45-90 Triangle
      4. 4
        30-60-90 Triangles
      5. 5
        The Area of a 45-45-90 Triangle
      6. 6
        The Area of a 30-60-90 Triangle
      7. 7
        The Area of an Equilateral Triangle
      8. 8
        Proving Triangle Theorems
      9. 9
        Proofs Involving Isosceles Triangles
      10. 10
        Medians and Centroids of Triangles
      11. 11
        Proofs Involving Medians and Centroids
    2. 2.4.2. Quadrilaterals
      1. 1
        Diagonals of Squares
      2. 2
        Properties of Parallelograms
      3. 3
        Proving Properties of Parallelograms
      4. 4
        Proving Criteria for Parallelograms and Rectangles
    3. 3.4.3. Trigonometry
      1. 1
        Angles and Sides in Right Triangles
      2. 2
        The Trigonometric Ratios
      3. 3
        Calculating Trigonometric Ratios Using the Pythagorean Theorem
      4. 4
        Calculating Side Lengths of Right Triangles Using Trigonometry
      5. 5
        Calculating Angles in Right Triangles Using Trigonometry
      6. 6
        Modeling With Trigonometry
      7. 7
        The Reciprocal Trigonometric Ratios
      8. 8
        Trigonometric Ratios in Similar Right Triangles
      9. 9
        Trigonometric Functions of Complementary Angles
      10. 10
        Special Trigonometric Ratios
      11. 11
        Calculating the Area of a Right Triangle Using Trigonometry
      12. 12
        Solving Multiple Right Triangles Using Trigonometry
  5. 5.Solid Geometry
    1. 1.5.1. Introduction to Solid Geometry
      1. 1
        Identifying Three-Dimensional Shapes
      2. 2
        Faces, Vertices, and Edges of Polyhedrons
      3. 3
        Nets of Polyhedrons
      4. 4
        Finding Surface Areas Using Nets
      5. 5
        The Distance Formula in Three Dimensions
      6. 6
        Euler's Formula for Polyhedra
      7. 7
        The Five Platonic Solids
      8. 8
        Surface Areas and Volumes of Similar Solids
    2. 2.5.2. Rectangular Solids and Pyramids
      1. 1
        Volumes of Cubes
      2. 2
        Surface Areas of Cubes
      3. 3
        Face Diagonals of Cubes
      4. 4
        Diagonals of Cubes
      5. 5
        Volumes of Rectangular Solids
      6. 6
        Surface Areas of Rectangular Solids
      7. 7
        Diagonals of Rectangular Solids
      8. 8
        Volumes of Pyramids
      9. 9
        Surface Areas of Pyramids
    3. 3.5.3. Non-Polyhedrons
      1. 1
        Volumes of Cylinders
      2. 2
        Surface Areas of Cylinders
      3. 3
        Volumes of Right Cones
      4. 4
        Slant Heights of Right Cones
      5. 5
        Surface Areas of Right Cones
      6. 6
        Volumes of Spheres
      7. 7
        Surface Areas of Spheres
      8. 8
        Conical Frustums
      9. 9
        Volumes of Revolution
  6. 6.Probability & Combinatorics
    1. 1.6.1. Introduction to Probability
      1. 1
        Sets
      2. 2
        Probability From Experimental Data
      3. 3
        Sample Spaces and Events in Probability
      4. 4
        Single Events in Probability
      5. 5
        The Complement of an Event
      6. 6
        Venn Diagrams in Probability
      7. 7
        Geometric Probability
    2. 2.6.2. Compound Events in Probability
      1. 1
        The Union of Sets
      2. 2
        The Intersection of Sets
      3. 3
        Compound Events in Probability From Experimental Data
      4. 4
        Computing Probabilities for Compound Events Using Venn Diagrams
      5. 5
        Computing Probabilities of Events Containing Complements Using Venn Diagrams
      6. 6
        Computing Probabilities for Three Events Using Venn Diagrams
      7. 7
        The Addition Law of Probability
      8. 8
        Applying the Addition Law With Event Complements
      9. 9
        Mutually Exclusive Events
    3. 3.6.3. Conditional Probability
      1. 1
        Conditional Probabilities From Venn Diagrams
      2. 2
        Conditional Probabilities From Tables
      3. 3
        The Multiplication Law for Conditional Probability
      4. 4
        The Law of Total Probability
      5. 5
        Tree Diagrams for Dependent Events
      6. 6
        Tree Diagrams for Dependent Events: Applications
      7. 7
        Independent Events
      8. 8
        Tree Diagrams for Independent Events
    4. 4.6.4. Combinatorics
      1. 1
        The Rules of Sum and Product
      2. 2
        Factorials
      3. 3
        Factorials in Variable Expressions
      4. 4
        Ordering Objects
      5. 5
        Permutations
      6. 6
        Combinations
      7. 7
        Computing Probabilities Using Combinatorics